Portfolio Management and Futures

As a portfolio manager, you are responsible for a $150 million portfolio, 90 percent of which is invested in equities, with a portfolio beta of 1.25. You are utilizing the S&P 500 as your passive benchmark. Currently the S&P 500 is valued at 1202. The value of the S&P 500 futures contract is equal to $250 times the value of the index. The beta of the futures contract is 1.0.

(a) If you anticipate a cash inflow of $2 million next week, how many futures contracts should you buy or sell in order to mitigate the effect of this inflow on the portfolio's performance?
(b) If you anticipate a cash outflow of $5 million next week, how many futures contracts should you buy or sell in order to mitigate the effect of this outflow on the portfolio's performance?
(c) How many contracts should you buy or sell in order to increase the portfolio beta to 1.30?
(d) How many contracts should you buy or sell in order to reduce the portfolio beta to 0.80?